# Characterization of Kurtz randomness by a differentiation theorem

News
Dec 25, 2012, Published
Aug 8, 2012, Published online
July 12, 2012, Accepted with a minor revision
Dec 23, 2011, Need to fix it
Oct 18, 2011, Submitted to a Journal

Title
Characterization of Kurtz randomness by a differentiation theorem

Type
Fullpaper

Journal
Theory of Computing Systems: Volume 52, Issue 1 (2013), Page 113-132
The page in TOCS

Abstract
Brattka, Miller and Nies showed that some major algorithmic randomness notions are characterized via differentiability.
The main goal of this paper is to characterize Kurtz randomness by a differentiation theorem on a computable metric space.
The proof shows that characterization by integral tests plays an essential part and shows that how randomness and differentiation are connected.